- #1
tpm
- 67
- 0
it's a curiosity more than a HOmework, given the integral:
[tex]\int_{-\infty}^{\infty}dx e^{if(x)+iwx}=g(w)[/tex]
Where g(w) can be viewed as the Fourier transform of exp(if(x)) then my question is if we can prove g(w) satisfies the ODE:
[tex]-if'(x)\frac{\partial g(w)}{\partial w}+wg(w)=0[/tex]
for simplicity we can impose [tex]exp(if(\infty))=0[/tex] and the same for
-oo
[tex]\int_{-\infty}^{\infty}dx e^{if(x)+iwx}=g(w)[/tex]
Where g(w) can be viewed as the Fourier transform of exp(if(x)) then my question is if we can prove g(w) satisfies the ODE:
[tex]-if'(x)\frac{\partial g(w)}{\partial w}+wg(w)=0[/tex]
for simplicity we can impose [tex]exp(if(\infty))=0[/tex] and the same for
-oo